The word Ainu is Quenya and is related to words for "holiness" such as aina; the female form (for beings like Melian or Árien, is given as Aini. Supposedly it is derived from the original Valarin word for Ainur which was Ayanûz. They are also referred to as Great Ones or Holy Ones.
Quenya
Ainu
holy one, angelic spirit
ainu
noun. holy one, spirit, holy one, angelic spirit (m.); [ᴱQ.] (pagan) god
ainur
Ainur
ainulindalë
proper name. Music of the Ainur
-a
it is said
-r nominative plural ending regularly used on nouns ending in -a, -i, -ië, -o, -u, e.g. Ainur, Valar, tier. Occasionally it is added also to nouns ending in -ë (that normally take the ending -I in the pl.). This seems to regularly happen in the case of nouns in -lë (see #fintalë, mallë, tyellë), sometimes also otherwise (see Ingwë, wendë, essë #1). This plural ending was ("it is said") first used by the Noldor (PM:402).
aina
holy
aina (2) adj "holy" (AYAN), derived from Ainu. Adopted and adapted from Valarin. According to VT43:32, the word is "obsolete, except in Ainur", apparently suggesting that airë or airëa (q.v.) was the normal term for "holy" in later Quenya. However, Tolkien repeatedly used aina in his translation of the Litany of Loreto: Aina Fairë "Holy Spirit", Aina Neldië "Holy Trinity", Aina Maria "Holy Mary", Aina Wendë "Holy Virgin". He also used Aina Eruontari for "holy Mother" in his rendering of the Sub Tuum Praesidium(WJ:399, FS, SA, VT43:32, VT44:5, 12, 17-18)
lindalë
music
lindalë noun "music". Cf. Ainulindalë "Music of the Ainur". (The word is cited as lindelë in the printed Etymologies, entry LIN2, but according to VT45:27, this is a misreading for lindalë in Tolkien's manuscript.) The word lindalë may argue the existence of a verbal stem #linda- "sing, make music".
lindalë
noun. music
aira
holy
aira (2) adj. "holy"; see airë #1
airë
holy
airë (1) adj. "holy", #Airefëa "the Holy Spirit" (VT43:37, dative airefëan on the previous page), airetári or Airë Tári "holy queen" (a title of Varda, PM:363), genitive aire-tário "holy-queen's" (Nam, RGEO:67). However, according to PM:363, airë is the noun "sanctity", while aira is the adjective "holy". VT43:14 refers to an etymological note of "Sept.-Oct. 1957" where airë is said to be a noun "sanctity, holiness", and the adjective "holy" is given as airëa. However, the verb #airita- "hallow" seems to be formed from an adjective airë, airi- "holy". Evidently airë can function as both adjective ("holy") and noun ("holiness"); if so airë as adj. could represent a primitive adjective gaisi, whereas airë as noun may descend from gaisē. The former but not the latter would have the stem airi- (as observed in the derived verb #airita-), and compounds like airetári (rather than *airitári) would seem to contain properly the noun "holiness".
airëa
holy
airëa adj. "holy"; see airë.
aista
holy
aista (1) adj. "holy" (VT43:37)
lindelë
music
lindelë noun "music" (LIN2, LT1:258 lindalë in Ainulindalë). According to VT45:27, lindelë in the printed Etymologies (entry LIN2) is a misreading for lindalë in Tolkien's manuscript.
Ainu noun "holy one, angelic spirit"; fem. Aini (AYAN, LT1:248); "one of the 'order' of the Valar and Maiar, made before Eä"; pl. Ainur is attested. Adopted and adapted from Valarin ayanūz(WJ:399). In the early "Qenya Lexicon", ainu was glossed "a pagan god", and aini was similarly "a pagan goddess", but as Christopher Tolkien notes, "Of course no one within the context of the mythology can call the Ainur 'pagan' " (LT1:248). Ainulindalë noun "Music of the Ainur" (SA:lin #2), the First History (WJ:406), the Song of Creation (AYAN)